The generalized Borwein conjecture. II. Refined q-trinomial coefficients

Refined q-trinomial coefficients and character identities

A refinement of the q-trinomial coefficients is introduced, which has a very powerful iterative property. This ``T-invariance'' is applied to derive new Virasoro character identities related to the exceptional simply-laced Lie algebras E_6,E_7 and E_8.

Refined $q$-Trinomial Coefficients and Two Infinite Hierarchies of $q$-Series Identities

We will prove an identity involving refined $q$-trinomial coefficients. We then extend this identity to two infinite families of doubly bounded polynomial identities using transformation properties of the refined $q$-trinomials in an iterative fashion in the spirit of Bailey chains. One of these two hierarchies contains an identity which is equivalent to Capparelli's first Partition Theorem.

有限Kleshchev双分拆与$q$-三项式系数

Finite Kleshchev bipartitions and $q$-trinomial coefficients

通过限制双分拆的最大部分，研究Kleshchev双分拆的计数函数，并证明其与Andrews和Baxter引入的两族$q$-三项式系数相关。